Food waste disposers in sinks and other types of waste grinding devices are commonly used with a supply of flushing water that transports the ground material through a drainage pipe into a waste disposal system. Because of clogging problems, such disposers have generally not been operated without water. However, many wastes can more efficiently be recovered, recycled, or disposed of if they are maintained in a dry state. Medical wastes such as rubber gloves are difficult to grind in existing equipment because of the tendency for such materials to clog, wedge and jam the disposer. Such materials tend to orient themselves transversely to the blades and are thus not readily disposed of. A need has thus existed for devices that are capable of efficiently grinding wastes such as thin-sectioned rubber materials.